@Article{JPDE-38-80,
author = {Chen , Wenjing and Wang , Zexi},
title = {On a Nonhomogeneous $N$-Laplacian Problem with Double Exponential Critical Growth},
journal = {Journal of Partial Differential Equations},
year = {2025},
volume = {38},
number = {1},
pages = {80--100},
abstract = {<p style="text-align: justify;">This paper is devoted to studying the existence and multiplicity of nontrivial
solutions for the following boundary value problem $$\begin{cases} -{\rm div}(\omega(x)|\nabla u(x)|^{N-2}\nabla u(x))=f(x,u)+\epsilon h(x), &amp; {\rm in} \ B; \\ u=0, &amp; {\rm on} \ \partial B, \end{cases}$$where $B$ is the unit ball in $\mathbb{R}^N,$ the radial positive weight $ω(x)$ is of logarithmic type
function, the functional $f(x,u)$ is continuous in $B×\mathbb{R}$ and has double exponential critical growth, which behaves like ${\rm exp}\{e^{\alpha|u|^{\frac{N}{N-1}}} \}$ as $|u| → ∞$ for some $α &gt; 0.$ Moreover, $ϵ&gt;0,$ and the radial function $h$ belongs to the dual space of $W^{1,N}_{0,rad}(B)$ $h\ne 0.$</p>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v38.n1.5},
url = {http://global-sci.org/intro/article_detail/jpde/23953.html}
}